1. Stochastic Simulations
Production Scheduling
Scheduling
Stochastic Simulations
Hy Nguyen
Tyler Tsang
Everyone
Haohan Xu
Jake Poliner

2. Outline 01. 02. 03. 04. Stochastic Simulation
Minimize Weighted Makespan
03.
Minimize Tardiness
Haohan
04.
Minimize Weighted Tardiness

3. These can be hard (or even NP hard) to solve for optimal schedules
Objective
Throughout the class we have primarily focused on deterministic scheduling problems
These can be hard (or even NP hard) to solve for optimal schedules
Test different stochastic situations to see how optimal schedule changes when there is randomness involved
Normal and exponential distributions
Varying variances
Haohan 0:40

4. Weighted completion Tardiness Weighted Tardiness
Three Scheduling Problems
Weighted completion
Tardiness
Weighted Tardiness
Haohan 0:50

5. For each one testing 4 stochastic scenarios Normal Low Var
Three Scheduling Problems
For each one testing 4 stochastic scenarios
Normal Low Var
Normal High Var
Normal High Var for low processing time and Low Var for high processing time
Exponential
Hy 1:20

6. Generate all permutations ordering of jobs
Testing Methodology
Generate all permutations ordering of jobs
For each permutation, ran 100,000 simulations and computed average objective function
Brute forced permutations
Returned the schedule with the objective function best minimized
Hy 1:42

7. Minimize Weighted Makespan
Tyler

8. Normally solved by weighted shortest processing time Optimal schedules
Minimize Weighted Makespan
Normally solved by weighted shortest processing time
Optimal schedules
2 – 6 – 3 – 5 – 7 – 4 – 1
2 – 6 – 5 – 3 – 7 – 4 – 1
Tyler

9. Minimize Weighted Makespan: Stochastic Results
Optimal Schedule
Normal Low Var
Normal Mix
Normal High Var
Exponential
Tyler

10. Minimize Tardiness Hy

11. Need to use a dynamic processing algorithm to solve Optimal schedule:
Minimize Tardiness
Need to use a dynamic processing algorithm to solve
Optimal schedule: Hy

12. Optimal Schedule Normal Low Var Normal Mix Normal High Var Exponential
Minimize Tardiness: Stochastic Results
Optimal Schedule
Normal Low Var
Normal Mix
Normal High Var
Exponential Hy

13. Minimize Weighted Tardiness
Tyler

14. Need to use a dynamic processing algorithm to solve
Minimize Weighted Tardiness
Is NP Hard
Need to use a dynamic processing algorithm to solve
Optimal schedule:
Tyler

15. Optimal Schedule Normal Low Var Normal Mix Normal High Var Exponential
Minimize Weighted Tardiness: Stochastic Results
Optimal Schedule
Normal Low Var
Normal Mix
Normal High Var
Exponential
Tyler 3:20

16. Normal distribution had results very similar to deterministic
Conclusions
Normal distribution had results very similar to deterministic
As Variance grew the optimal schedule tended to change more
Exponential distribution tended to have very different results from deterministic
We think this is because there is symmetry in the normal distribution whereas the exponential distribution is not symmetrical
The inclusion of randomness makes finding the optimal schedule very hard, and most if not all are NP hard Hy

17. Conclusions
Exponential distribution tended to have very different results from deterministic
We think this is because there is symmetry in the normal distribution whereas the exponential distribution is not symmetrical Hy

18. However, we still find immense value in being able to:
Limits of Experiment
As there are more jobs, our brute force method becomes more unfeasible.
However, we still find immense value in being able to:
Write flexible code
Obtain empirical answers Hy

19. Test further distributions, preferably ones nonsymmetrical
Potential Future Tests
Test further distributions, preferably ones nonsymmetrical
Make different scenarios where the variance is not related to processing time
Parallel and other multi machine schedules
Hy 1:42

20. THANK YOU!
Questions & Comments Hy